103/5f=8-1/2f

Solution for 103/5f=8-1/2f equation:

103/5f=8-1/2f

We move all terms to the left:

103/5f-(8-1/2f)=0


Domain of the equation: 5f!=0

f!=0/5

f!=0

f∈R



Domain of the equation: 2f)!=0

f!=0/1

f!=0

f∈R


We add all the numbers together, and all the variables

103/5f-(-1/2f+8)=0

We get rid of parentheses

103/5f+1/2f-8=0

We calculate fractions


206f/10f^2+5f/10f^2-8=0

We multiply all the terms by the denominator


206f+5f-8*10f^2=0

We add all the numbers together, and all the variables

211f-8*10f^2=0

Wy multiply elements

-80f^2+211f=0

a = -80; b = 211; c = 0;
Δ = b2-4ac
Δ = 2112-4·(-80)·0
Δ = 44521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{44521}=211$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(211)-211}{2*-80}=\frac{-422}{-160}
=2+51/80
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(211)+211}{2*-80}=\frac{0}{-160}
=0
$